I wouldn't run a hard plastic Firestone tire on my lawnmower, let alone on my car. No, the issue goes way back before the tire blowout deal. That was just a case of I told you so showing up a number of years later.
You said new tires, but do you mean new a few days ago when you started driving the car, or new 2 years ago when you parked the car? If you let it sit on the tires, they have flat spots, and they are destroyed.
There is also an issue called load blance, and it would be typical of a Firestone product: The tires will static/bubble balance, but when operated under a load. That could be the issue more than flat spots because of the problem in one speed zone. Again, flat spots can be the issue because the problem goes away after 45 because centrifigual force irons out the flat area. Then again, I'm only guessing that the problem goes away above 45 because you didn't say whether or not it irons out above 50 mph.
It's a safe bet that it isn't the brake components because there is a good chance that they brakes would pulsate. If I were dealing with the car, one sure bet would be that the firestones would be in the s/can, and that would solve that aspect on tire troubleshooting.
Let's pretend that I loved firestone tires,a nd I could not find a donor set of tires. (Even in Maine--I hanged out every summer in Rockport--you should be able to find a borrowed set because there are a bezillion 14's or 15's that will bolt up.) If I couldn't, it's a toss up of whether I would get would get 4 used tires that held air, mount/balance them, or replace the tires.
If the tires are brand new, as in being bought a few days ago, they should have a warranty. Oh yeah, that's right--they're firestones.